With regards to wave functions

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SUMMARY

The discussion confirms that displacement-distance and displacement-time graphs for wave forms will appear identical if the wave is sinusoidal or if the wave propagates without dispersion. The mathematical representation of the wave is given as x = asin(omega*t), where 'a' is the amplitude and 'omega' is the angular frequency. The key condition for the graphs to match is that the wave speed remains constant and independent of frequency.

PREREQUISITES
  • Understanding of sinusoidal waveforms
  • Knowledge of wave propagation and dispersion
  • Familiarity with angular frequency and amplitude
  • Ability to interpret displacement-distance and displacement-time graphs
NEXT STEPS
  • Study the properties of sinusoidal waves in detail
  • Research wave propagation and the concept of dispersion
  • Learn about the mathematical representation of wave functions
  • Explore graphical analysis of waveforms and their characteristics
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Students of physics, wave mechanics enthusiasts, and educators looking to deepen their understanding of wave behavior and graph interpretation.

niggawut
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If I draw a displacement-distance graph and a displacement-time for two wave forms, will both graphs look the same? With the exception of the x-axis label.
 
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yes I'm fairly sure they will be identical. Are the waves of the form x = asin(omega*t) ?
 
They will be the same provided that...
EITHER the waveform (shape of displacement against time graph) is sinusoidal,
OR, for any waveform, the wave propagates without dispersion, which means that the wave speed is independent of waveform, i.e. independent of frequency for a sinusoid.
 

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